A question for iterated Galois groups in arithmetic dynamics

TL;DR

The paper explores a broad question about the size of iterated Galois groups in algebraic dynamical systems, analyzing specific cases to understand their properties and implications.

Contribution

It introduces a general framework for investigating the size of iterated Galois groups in arithmetic dynamics and discusses particular instances of this question.

Findings

Identifies key cases where the size of Galois groups can be characterized.

Provides insights into the relationship between dynamical systems and Galois theory.

Suggests directions for future research in the area.

Abstract

We formulate a general question regarding the size of the iterated Galois groups associated to an algebraic dynamical system and then we discuss some special cases of our question.